Problem: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 8x - 9$ and $ BC = 9x - 17$ Find $AC$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {8x - 9} = {9x - 17}$ Solve for $x$ $ -x = -8$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 8({8}) - 9$ $ BC = 9({8}) - 17$ $ AB = 64 - 9$ $ BC = 72 - 17$ $ AB = 55$ $ BC = 55$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {55} + {55}$ $ AC = 110$